164 Prof. E. Rutherford on Radioactivity 



the intensity of the radiation from radio-active plates and 

 cylinders, a brief theoretical discussion will be given of the 

 relation that exists between the intensity of the radiation, the 

 area of the active surface, and the maximum current through 

 the gas. 



Two cases will be considered — 



(I.) When the radiation is given out uniformly from a 



plane surface and the current through the gas is 



measured between two parallel planes. 



(II.) When the radiation is given out from a cylinder and 



the current measured between concentric cylinders. 



Case I. — We will first consider the case of a uniformly 



radio-active plate C, of area S, which is placed between two 



large parallel plates A and B (fig. 2 a). 



Fig. 2 a. Fig. 2 b. 



fir 1 * 



We will suppose the plate C to be of large dimensions 

 compared with the distance d of the plate C from A, and to 

 give out radiation equally from all points of its surface. The 

 gas is ionized by the passage of the radiation through it, 

 and the ions produced travel to the plates A and C under the 

 influence of the electric field. 



In consequence of the energy required to ionize the gas, the 

 intensity of the radiation diminishes in its passage through it. 



Suppose the radiation is homogeneous in character, and that 

 X is the coefficient of absorption of the radiation by the gas. 

 Let I be the intensity of the radiation at the surface of the 

 plate. Since the plate is large compared with the distance <i, 

 the value of the intensity may be considered approximately 

 equal at equal distances from the surface C. In consequence of 

 the absorption of the radiation by the gas, the intensity I at a 

 distance x from the active plate is given by 



I = I e-^. 



Let dn be the number of ions produced per second between 

 two planes parallel to C and distant x and x-\-dx from it. 

 Since the rate of production of ions is proportional to the 



